Consider the two curves
Cy=4x
Cx+y2-6x+1=0
Then,
C and C touch each other only at one point
B)
C and C touch each other exactly at two points
If0<x<1,then
1+x{xcoscotx+sincotx}2-1]2=
The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit
vectors db,c such that
ab=bc=ca=
2
Then,the volume of the parallelopiped is
Let a and b be non-zero real numbers.Then, the equation
ax2+by2+cx-5xy+6y=0
represents
A) four straight lines, when c =0 and ab are of the same sign
Bt
two straight lines and a circle, when a =b,and c is of sign opposite to that of a
C
two straight lines and a hyperbola, when a and b are of the same sign and c is
of sign opposite to that of a
D
a circle and an ellipse, when a and b are of the same sign and c is of sign
opposite to that of a
Let
x-1
gx=
0<x<2m and n are integersm0n>0and
logcosx-1
let p be the left hand derivative ofx-1| at x=1.
If lim g(x= p,then
- n=1m=1
- n=1,m=-1
- n=2m=2
- n>2m=n
The total number of local maxima and local minima of the function
2+x3-3<x-1
fx=
213
-1<x<2
is
A straight line through the vertex P of a triangle PQR intersects the side QR at
the point S and the circumcircle of the triangle PQR at the point T.If S is not the
centre of the circumcircle,then
1
1
2
Let Px1yand Qxy)y<0y2<0,be the end points of the latus rectum of
the ellipse x2+4y=4.The equations of parabolas with latus rectum PQ are
- x2+23y=3+3
- x2-23y=3+3
- x2+23y=3-3
- x2-23y=3-3
Let
Sn=
n
n
for n=1,2,3,.Then,
Let fx) be a non-constant twice differentiable function defined on -,) such
that fx=f1-x)andf
=0.Then
Afx vanishes at least twice on[01]
Let f and g be real valued functions defined on interval -1,1 such that gx) is
continuousg00g0=0,g00,andfx=gxsinx.
STATEMENT-1lim[gxcotx-g0 cosec x]=f0.
x-0
and
STATEMENT-2:f0=g0.
A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct
explanation for STATEMENT-1
B
STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a
correct explanation for STATEMENT-1
C
STATEMENT-1 is True,STATEMENT-2 is False
D) STATEMENT-1 is False,STATEMENT-2 is True
Consider three planes
Px-y+z=1
Px+y-z=-1
P3x-3y+3z=2.
Let LLL be the lines of intersection of the planes P and P3,P3 and P1
and P and P,respectively.
STATEMENT-1:At least two of the lines LL and L3 are non-parallel.
and
STATEMENT-2:The three planes do not have a common point.
A) STATEMENT-1 is True, STATEMENT-2 is True;STATEMENT-2 is a correct
explanation for STATEMENT-1
B
STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a
correct explanation for STATEMENT-1
CSTATEMENT-1 is True,STATEMENT-2 is False
D STATEMENT-1 is False,STATEMENT-2 is True
0
Consider the system of equations
x-2y+3z=-1
-x+y-2z=k
x-3y+4z=1.
STATEMENT-1 The system of equations has no solution for k+3.
and
1
3
-1
STATEMENT-2:The determinant
-1
-2
k
0fork3.
1
4
1
A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct
explanation for STATEMENT-1
B
STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a
correct explanation for STATEMENT-1
Consider the system of equations
ax+by=0,cx+dy=0,wherea,bc,de{0,1}.
STATEMENT-1: The probability that the system of equations has a unique
3
solution is
8
and
STATEMENT-2:The probability that the system of equations has a solution is 1.
The equation of circle C is
Ax-232+y-1=1
I=2+x+8-x8
2
Cx-32+y+12=1
Dx-3+y-12=1
0
Points E and F are given by
13.3. (3,0
3
Equations of the sides QR,RP are
2
2
1
If f-102=22thenf-102=
42
42
42
42
The area of the region bounded by the curve y =fx),the x-axis,and the lines x=a
andx=bwhere-<a<b-2,is
The number of elements in the set A B C is
A
0
B)
1
Let z be any point in ABnC.Thenz+1-i|+z-5-i|lies between
A25 and29
B
30 and 34
C35 and 39
D40and44
Students I, II and III perform an experiment for measuring the acceleration due to
gravity (g) using a simple pendulum. They use different lengths of the pendulum
and/or record time for different number of oscillations. The observations are shown in
the table.
Least count for length=0.1 cm
Least count for time = 0.1 s
Student
Length of the
Number of
Total time for
Time
pendulum (cm)
oscillations (n)
(n) oscillations (s)
period (s)
I
64.0
8
128.0
16.0
II
64.0
4
64.0
16.0
III
20.0
4
36.0
9.0
If EEl and El are the percentage errors in g,i.e.
g
and III respectively,
A
E=0
BE is minimum
Figure shows three resistor configurations R1,R2 and R3 connected to 3 V battery.If
the power dissipated by the configuration R1,R2 and R3 is P1,P2 and P3,
respectively,then
Figure:
12
12
12
12
3V
12
3V
12
12
12
3V
12
12
12
12
12
12
R1
R2
R3
- P1>P2>P3
- P1>P3>P2
- P2>P1>P3
- P3>P2>P1
Which one of the following statements is WRONG in the context of X-rays generated
from a X-ray tube?
A) Wavelength of characteristic X-rays decreases when the atomic number of the
target increases
B
Cut-off wavelength of the continuous X-rays depends on the atomic number of
the target
C
Intensity of the characteristic X-rays depends on the electrical power given to
the X-ray tube
D
Cut-off wavelength of the continuous X-rays depends on the energy of the
electrons in the X-ray tube
Two beams of red and violet colours are made to pass separately through a prism
angle of the prism is 60). In the position of minimum deviation, the angle of
refraction will be
A30for both the colours
A spherically symmetric gravitational system of particles has a mass density
Pofor rR
0=
0forr>R
where Po is a constant.A test mass can undergo circular motion under the influence
of the gravitational field of particles.Its speed V as a function of distance
r0<r<) from the centre of the system is represented by
(A
Two balls,having linear momenta p=pi and p=-piundergo a collision in free
space. There is no external force acting on the balls.Let p and pbe their final
momenta.The following options) is(are) NOT ALLOwED for any non-zero value of
paabbcandc
Ap=ai+bj+ck
Bp=ch
p=ai+bj
p=ck
Cp=ai+bj+ch
Dp=ai+bj
p=ai+bj-ch
P=ai+bj
A particle of mass m and charge q,moving with velocity V enters Region II normal to
the boundary as shown in the figure. Region II has a uniform magnetic field B
perpendicular to the plane of the paper.The length of the Region II is .Choose the
correct choice(s).
Figure:
Region I
Region II
Region III
XXXX
XXXX
XXXX
XXXX
XXXX
m
m
C
m
D
Time spent in Region II is same for any velocity V as long as the particle returns
to Region I
In a Young's double slit experiment, the separation between the two slits is d and the
wavelength of the light is .The intensity of light falling on slit 1 is four times the
intensity of light falling on slit 2.Choose the correct choice(s).
A) If d =,the screen will contain only one maximum
B If <d<2,at least one more maximum besides the central maximum will
be observed on the screen
C
If the intensity of light falling on slit 1 is reduced so that it becomes equal to
that of slit 2, the intensities of the observed dark and bright fringes will
increase
D) If the intensity of light falling on slit 2 is increased so that it becomes equal to
that of slit 1, the intensities of the observed dark and bright fringes will
increase
STATEMENT-1
In a Meter Bridge experiment, null point for an unknown resistance is measured.
Now, the unknown resistance is put inside an enclosure maintained at a higher
temperature. The null point can be obtained at the same point as before by
decreasing the value of the standard resistance.
and
STATEMENT-2
Resistance of a metal increases with increase in temperature.
A) STATEMENT-1 is True, STATEMENT-2 is TrueSTATEMENT-2 is a correct
explanation for STATEMENT-1
B
STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a
correct explanation for STATEMENT-1
C
STATEMENT-1 is True, STATEMENT-2 is False
(D STATEMENT-1 is False,STATEMENT-2 is True
Answer
(V)
B)
STATEMENT-1
An astronaut in an orbiting space station above the Earth experiences weightlessness.
and
STATEMENT-2
An object moving around the Earth under the influence of Earth's gravitational force
is in a state offree-fall.
STATEMENT-1
Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and
identical dimensions are simultaneously allowed to roll without slipping down an
inclined plane from the same height. The hollow cylinder will reach the bottom of the
inclined plane first.
and
STATEMENT-2
By the principle of conservation of energy, the total kinetic energies of both the
cylinders are identical when they reach the bottom of the incline.
STATEMENT-1
The stream of water flowing at high speed from a garden hose pipe tends to spread
like a fountain when held vertically up, but tends to narrow down when held
vertically down.
and
STATEMENT-2
In any steady flow of an incompressible fluid, the volume flow rate of the fluid
remains constant.
(A STATEMENT-1 is True, STATEMENT-2 is True;STATEMENT-2 is a correct
explanation for STATEMENT-1
B)STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a
correct explanation for STATEMENT-1
(C
STATEMENT-1 is True,STATEMENT-2 is False
As the bubble moves upwards, besides the buoyancy force the following forces are
acting on it
A)Only the force of gravity
B) The force due to gravity and the force due to the pressure of the liquid
C
The force due to gravity, the force due to the pressure of the liquid and the force
due to viscosity of the liquid
D
The force due to gravity and the force due to viscosity of the liquid
When the gas bubble is at a height y from the bottom,its temperature is
The quantum number n of the state finally populated in He* ions is
A
2
B3
C4
D5
The wavelength of light emitted in the visible region by He* ions after collisions with
H atoms is
A
6.510m
B5.610m
-7
The ratio of the kinetic energy of the n =2 electron for the H atom to that of Heion
is
The speed of the block at point B immediately after it strikes the second incline is
A60 m/s
The speed of the block at point C, immediately before it leaves the second incline is
A120m/s
If collision between the block and the incline is completely elastic, then the vertical
upward) component of the velocity of the block at point B, immediately after it
strikes the second incline is
A30 m/s
B15 m/s
Hyperconjugation involves overlap of the following orbitals
(A
0-0
The major product of the following reaction is
MeBr
PhS Na
dimethylformamide
NO₂
Me
SPh
Me
SPh
F
F
Aqueous solution of NaSO on reaction with Cl gives
A
NaSO6
Native silver metal forms a water soluble complex with a dilute aqueous solution of
NaCN in the presence of
Anitrogen
Under the same reaction conditions, initial concentration of 1.386 mol dm of a
substance becomes half in 40 seconds and 20 seconds through first order and zero
k
order kinetics, respectively.Ratio
of the rate constants for first order (k) and
ko
zero order (k) of the reactions is
- 0.5 moldm
- 1.0 moldm³
- 1.5 moldm³
- 2.0 mol-dm
The correct statement(s) about the compound given below is (are)
H
CH₃
H3C
CI
H
The correct statement(s) concerning the structures E,F and G is (are)
H3C-
O
H3C-
HO
H3C-
CH₃
H3C
CH₃
H3C
CH₃
H3C
OH
(E)
(F)
(G)
A
E, F and G are resonance structures
BE,F and E,G are tautomers
C)
F and G are geometrical isomers
D
F and G are diastereomers
A gas described by van der Waals equation
A) behaves similar to an ideal gas in the limit of large molar volumes
B) behaves similar to an ideal gas in the limit of large pressures
C is characterised by van der Waals coefficients that are dependent on the
identity of the gas but are independent of the temperature
D
has the pressure that is lower than the pressure exerted by the same gas
behaving ideally
STATEMENT-1:Bromobenzene upon reaction with Br/Fe gives 1,4-dibromobenzene
as the major product.
and
STATEMENT-2:In bromobenzene, the inductive effect of the bromo group is more
dominant than the mesomeric effect in directing the incoming
electrophile.
STATEMENT-1:Pb+ compounds are stronger oxidizing agents than Sn4+compounds.
and
STATEMENT-2: The higher oxidation states for the group 14 elements are more
stable for the heavier members of the group due to inert pair
effect'.
A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct
explanation for STATEMENT-1
B
STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a
correct explanation for STATEMENT-1
STATEMENT-1: The plot of atomic number y-axis) versus number of neutrons
x-axis) for stable nuclei shows a curvature towards x-axis from
the line of 45slope as the atomic number is increased.
and
STATEMENT-2: Proton-proton electrostatic repulsions begin to overcome attractive
forces involving protons and neutrons in heavier nuclides.
STATEMENT-1:For every chemical reaction at equilibrium, standard Gibbs energy
of reaction is zero.
and
STATEMENT-2: At constant temperature and pressure, chemical reactions are
spontaneous in the direction of decreasing Gibbs energy.
A STATEMENT-1 is True,STATEMENT-2 is True;STATEMENT-2 is a correct
explanation for STATEMENT-1
B
STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a
correct explanation for STATEMENT-1
The structure of the product I is
A
Me
Br
The structures of compounds J and K,respectively, are
The structure of product L is.
Among the following,the correct statement is
Among the following, the correct statement is
A Between NH and PH3,NH is a better electron donor because the lone pair of
electrons occupies spherical's'orbital and is less directional
B) Between NH and PH3,PH is a better electron donor because the lone pair of
electrons occupies sp orbital and is more directional
C Between NH and PH,NH is a better electron donor because the lone pair of
electrons occupies sp orbital and is more directional
D Between NH and PHPH is a better electron donor because the lone pair of
electrons occupies spherical's' orbital and is less directional
White phosphorus on reaction with NaOH gives PH as one of the products.This is a
The freezing point of the solution M is
A268.7K
B
268.5 K
C234.2K
D150.9K
0
The vapour pressure of the solution M is
A)39.3 mm Hg
Water is added to the solution M such that the mole fraction of water in the solution
becomes 0.9.The boiling point of this solution is
A)380.4 K
B)
376.2K
C375.5K
D354.7K
